A principle, central to quantum mechanics, which states that two
complementary parameters (such as position and momentum, energy
and time, or angular momentum and angular displacement) cannot
both be known to infinite accuracy; the more you know about
one, the less you know about the other.
It can be illustrated in a fairly clear way as it relates to
position vs. momentum: To see something (let's say an electron),
we have to fire photons at it; they bounce off and come back to
us, so we can "see" it. If you choose low-frequency photons, with
a low energy, they do not impart much momentum to the electron,
but they give you a very fuzzy picture, so you have a higher
uncertainty in position so that you can have a higher certainty in
momentum. On the other hand, if you were to fire very high-energy
photons (x-rays or gammas) at the electron, they would give you a
very clear picture of where the electron is (higher certainty in
position), but would impart a great deal of momentum to the
electron (higher uncertainty in momentum).
In a more generalized sense, the uncertainty principle tells
us that the act of observing changes the observed in fundamental
way.